“Africa is on the move… People are being lifted out of poverty, incomes are up (and) the middle class is growing,” he told a business summit.
He later visited a memorial for those killed in the 1998 US embassy bombing.
His schedule includes security talks with Kenya’s president Uhuru Kenyatta.
The trip which started on Friday has been described as a “homecoming” by Kenyan media.
It is Mr Obama’s first visit as president to the country where his father was born.
Crowds cheered Mr Obama’s motorcade as it travelled from the airport.
His first appearance in Nairobi on Saturday morning, was presiding over the opening of a Global Entrepreneurship Summit.
Africa needed to be a “future hub of global growth”, Mr Obama told young entrepreneurs and businesspeople, adding that governments had to ensure that corruption was not allowed to flourish.
He said Kenya had made “incredible progress” since his last visit.
“When I was here in Nairobi 10 years ago, it looked different from what it looks today,” he said.
Later, Mr Obama visited the memorial park on the site of the US embassy where 213 people were killed in an al-Qaeda truck bombing in 1998.
Twelve Americans and 34 local embassy workers died in the blast on the same day the US embassy in Dar es Salaam, Tanzania, was targeted killing 11 people.
Survivors attended as he laid a wreath.
Security is tight for Mr Obama’s visit with about 10,000 police officers deployed in Nairobi, major roads closed and US military planes patrolling overhead.
Security and Kenya’s counter-terrorism efforts are likely to dominate Mr Obama’s talks with President Kenyatta.
Kenya has been targeted by the militant Somalia-based Islamist group al-Shabab which killed at least 67 people in an attack on Nairobi’s Westgate shopping complex in 2013.
The group also staged an attack on the university in Garissa, northern Kenya, earlier this year in which 148 people died.
Although trade and security are featuring strongly in Mr Obama’s visit, he has also pledged to deliver a “blunt message” to African leaders about gay rights and discrimination.
Kenyans to Obama: ‘Spare us the gay talk’
On his arrival at Kenyatta International Airport in Nairobi, he was hugged by his half-sister Auma and later, at dinner, the president was joined by more relatives including “Mama Sarah”, who helped to raise his late father.
Mr Obama’s visit would have been diplomatically impossible when President Kenyatta faced charges at the International Criminal Court in The Hague, says the BBC’s Karen Allen in Nairobi.
The case against Mr Kenyatta has since been dropped and the way seems clear for a restoration of ties, she adds.
After his visit to Kenya, Mr Obama will travel on to Ethiopia where he will become the first US leader to address the African Union.